Henryk Fukś

Performance of data networks with random links

We investigate simplified models of computer data networks and examine how the introduction of additional random links influences the performance of these networks. In general, the impact of additional random links on the performance of the network strongly depends on the routing algorithm used in the network. Significant performance gains can be achieved if the routing is based on ‘geometrical distance’ or shortest path reduced table routing. With shortest path full table routing degradation of performance is observed.

EXACT RESULTS FOR DETERMINISTIC CELLULAR AUTOMATA TRAFFIC MODELS

We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generalized hypergeometric function. We show that the steady-state limit agrees with previously published results.

Packet delay in models of data networks

We investigate individual packet delay in a model of data networks with table-free, partial table and full table routing. We present analytical estimation for the average packet delay in a network with small partial routing table. Dependence of the delay on the size of the network and on the size of the partial routing table is examined numerically. Consequences for network scalability are discussed.

Modeling Diffusion of Innovations with Probabilistic Cellular Automata

We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.

A new class of automata networks

A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function IA on the interval [0, 1]. It is shown that any cellular automaton rule can be represented by a (nonunique) rule formulated in terms of a pair (p, IA). This new class of automata networks contains discrete systems which are not cellular automata. For a given p, a metric can be defined on the space of all rules which induces a metric on the space of all cellular automata rules.

MOTION REPRESENTATION OF ONE-DIMENSIONAL CELLULAR AUTOMATON RULES

Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete analogue of the source term. This new representation is general, but not unique, and can be used to represent, in a more visual way, any one-dimensional cellular automaton rule. A few illustrative examples are presented.

Active macromolecules of honey form colloidal particles essential for honey antibacterial activity and hydrogen peroxide production

Little is known about the global structure of honey and the arrangement of its main macromolecules. We hypothesized that the conditions in ripened honeys resemble macromolecular crowding in the cell and affect the concentration, reactivity, and conformation of honey macromolecules. Combined results from UV spectroscopy, DLS and SEM showed that the concentration of macromolecules was a determining factor in honey structure. The UV spectral scans in 200–400 nm visualized and allowed quantification of UV-absorbing compounds in the following order: dark > medium > light honeys (p < 0.0001). The high concentration of macromolecules promoted their self-assembly to micron-size superstructures, visible in SEM as two-phase system consisting of dense globules distributed in sugar solution. These particles showed increased conformational stability upon dilution. At the threshold concentration, the system underwent phase transition with concomitant fragmentation of large micron-size particles to nanoparticles in hierarchical order. Honey two-phase conformation was an essential requirement for antibacterial activity and hydrogen peroxide production. These activities disappeared beyond the phase transition point. The realization that active macromolecules of honey are arranged into compact, stable multicomponent assemblies with colloidal properties reframes our view on global structure of honey and emerges as a key property to be considered in investigating its biological activity.

Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata

AbstractThe mathematical analysis of the second-order phase transitions that occur in α-asynchronous cellular automata field is a highly challenging task. From the experimental side, these phenomena appear as a qualitative change of behaviour which separates a behaviour with an active phase, where the system evolves in a stationary state with fluctuations, from a passive state, where the system is absorbed in a homogeneous fixed state. The transition between the two phases is abrupt: we ask how to analyse this change and how to predict the critical value of the synchrony rate α. We show that an extension of the mean-field approximation, called the local structure theory, can be used to predict the existence of second-order phase transitions belonging to the directed percolation university class. The change of behaviour is related to the existence of a transcritical bifurcation in the local structure maps. We show that for a proper setting of the approximation, the form of the transition is predicted correctly and, more importantly, an increase in the level of local structure approximation allows one to gain precision on the value of the critical synchrony rate which separates the two phases.

Topological structure of dictionary graphs

We investigate the topological structure of the subgraphs of dictionary graphs constructed from WordNet and Moby thesaurus data. In the process of learning a foreign language, the learner knows only a subset of all words of the language, corresponding to a subgraph of a dictionary graph. When this subgraph grows with time, its topological properties change. We introduce the notion of the pseudocore and argue that the growth of the vocabulary roughly follows decreasing pseudocore numbers—that is, one first learns words with a high pseudocore number followed by smaller pseudocores. We also propose an alternative strategy for vocabulary growth, involving decreasing core numbers as opposed to pseudocore numbers. We find that as the core or pseudocore grows in size, the clustering coefficient first decreases, then reaches a minimum and starts increasing again. The minimum occurs when the vocabulary reaches a size between 103 and 104. A simple model exhibiting similar behavior is proposed. The model is based on a generalized geometric random graph. Possible implications for language learning are discussed.

Bifurcations of Local Structure Maps as Predictors of Phase Transitions in Asynchronous Cellular Automata

We show that the local structure approximation of sufficiently high order can predict the existence of second order phase transitions belonging to the directed percolation university class in α-asynchronous cellular automata.